Have you checked in the game's config file? There should be a framerate cap parameter in there saying "com_maxfps", make sure it's set to 0 (for uncapped framerate).
You can also find a parameter saying "RestrictGraphicsOptions" which you can set from 1 to 0, to give you more playroom with the in-game graphics.
Path to the config file should be something like: Steam\steamapps\common\call of duty black ops 3\players\
If the above doesn't work, specifically what other games does your PC play fine? If more lightweight games, have you made sure the PC is not overheating (with software such as HWMonitor)?